Find a regression model who's predictions are not that volatile

[jimjohn]

I haev a regression model with two independent variables. these two variables have historically proved to be a good predictor since the Adjusted R^2 = .707. However, for the most recent month and the month before, although the model has been predicting the correct movement of the independent variable, it has been overestimating the absolute value of that move. I'm trying to find a different regression model that may be less volatile so that it wouldn't predict such big changes but still be a decent predictor. I tried quadratic terms, I tried taking the ln of the dep variable but both cases I still get the high predicted value. Any ideas how I can find such a less-volatile model? Thanks guys!

[Hector Maletta]

I think, JimJohn, your approach is not the good one. You have a model that
has historically behaved well, but suddenly it has not behaved so well in
the last couple of months. The answer is not a modification of the model to
suit the change in the actual behavior of the dependent variable: perhaps
next months things return to the historical tendency and the old model
behaves well again.
The logical approach is asking WHY the dependent variable may have varied
differently in the most recent periods. The key question is whether the
difference is transient or an indication of a new trend, and (lacking
information about the future) this question can only be approached armed
with theoretical weapons and using additional empirical information.
Just adding a bit of purely statistical wisdom: regression analysis
estimates the expected value of a variable, plus/minus a random error.
Assuming all regression assumptions are valid, then in 95% of the cases the
random component would be within 2 standard errors, but that does not
preclude the occasional error falling beyond. It is in the nature of random
errors to have a distribution, and the distribution includes cases in the
tails of the curve, well beyond the confidence interval. With just one or
two months of wider deviation you cannot tell whether it is something real
or just pure chance.
From a more substantive point of view, any real process may not go forever.
As you fall from the 38th floor to the street below, a simple equation can
predict your position and speed at every successive fraction of a second
with amazing precision --except after that last fraction of a second in
which you hit the ground. Irving Fisher made millions in the NY stock
exchange in the 1920s, and famously predicted that the boom would persist
and persist, insisting in this view even after the 1929 crash (losing
millions, and causing others to lose more millions): he had a regression
equation predicting the Stock Exchange results of tomorrow based on data
available today; he just did not foresee the Great Depression, his equation
was just short term and did not include major shifts in the world economy,
and thus he thought the loss of a few points at the Exchange in that Black
day of 1929 was just a temporary glitch in an otherwise bullish market.
There is more on Heaven and Earth than one can catch with statistics, he
finally discovered.
Hector
-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
jimjohn
Sent: 10 July 2009 16:19
To: [hidden email]
Subject: Find a regression model who's predictions are not that volatile

I haev a regression model with two independent variables. these two
variables
have historically proved to be a good predictor since the Adjusted R^2 =
.707. However, for the most recent month and the month before, although the
model has been predicting the correct movement of the independent variable,
it has been overestimating the absolute value of that move. I'm trying to
find a different regression model that may be less volatile so that it
wouldn't predict such big changes but still be a decent predictor. I tried
quadratic terms, I tried taking the ln of the dep variable but both cases I
still get the high predicted value. Any ideas how I can find such a
less-volatile model? Thanks guys!
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